Question

Graph ​ y−5=−2/3(x+9) ​ using the point and slope given in the equation.

Use the line tool and select two points on the line.

Answer 1

Answer: There are several points you could use:

1. (0,-1)

2.(3,-3)

3. (6,-5)

4. (9,-7)

5.(-3,1)

(Just to name a few...)

Step-by-step explanation:

To check these, all you'd have to do is substitute each value in the coordinate. For example, to check if (9,-7) would satisfy the equation, you'd substitute 9 for x and -7 for y, as shown below:

(-7) - 5 = -2/3 (9 +9)

Next, you'd solve the equation. Since (-7) - 5 is basically the same as -7 + -5, or the opposite of 7+5 (which is 12), the answer for the left side would be -12.

Then, you would solve for the right. 9 + 9 is the same as 18. Using that knowledge, you could solve for the rest of the right side by multiplying -2/3 by 18, which is -12.

Since -12 = -12, we know that the coordinates (9,-7) satisfy the equation.

Answer 2

To graph the equation y - 5 = -2/3(x + 9), rewrite it in slope-intercept form and find the y-intercept. Use the slope -2/3 to determine another point on the line, and then draw a straight line through the points to graph the equation.

Step-by-step explanation:

To graph the equation y - 5 = -2/3(x + 9), we will first rewrite it in slope-intercept form, which is y = mx + b. Here, m represents the slope and b represents the y-intercept. The given equation can be transformed by adding 5 to both sides to isolate y, resulting in y = -2/3(x + 9) + 5.

Next, we find the point given by the equation, starting with x = -9 to make the equation simpler:

For x = -9, y = -2/3(-9 + 9) + 5 = 5. So, one point we can use is (-9, 5).

Now, we can use the slope, which is -2/3. This means that for every 3 units we move to the right (positive direction along the x-axis), we move 2 units down (negative direction along the y-axis). From our initial point (-9, 5), if we add 3 to x and subtract 2 from y, we get the next point:

Start at (-9, 5) and move to (-6, 3).

Finally, with these two points (-9, 5) and (-6, 3), we can draw a straight line using the point and slope information to graph the equation.